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Chapter 6 · Grade 12 Advanced
Applications of the Definite Integral
Integration's true power shows up here: areas, volumes, lengths, motion, work, and probability — all reduce to evaluating a definite integral.
Lessons
Lesson 1 · G12 6.1
Area Between Curves
Integrating the difference of two functions.
Open lesson → Lesson 2 · G12 6.2Volume Slicing Disks and Washers
Cross-section method for volumes.
Open lesson → Lesson 3 · G12 6.3Volumes by Cylindrical Shells
An alternative volume technique.
Open lesson → Lesson 4 · G12 6.4Arc Length and Surface Area
Lengths of curves and surfaces.
Open lesson → Lesson 5 · G12 6.5Projectile Motion
Modelling motion with integrals.
Open lesson → Lesson 6 · G12 6.6Applications to Physics and Engineering
Work, fluid pressure, centre of mass.
Open lesson → Lesson 7 · G12 6.7Probability
Continuous probability density functions.
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